Radical Classes of Lattice-Ordered Groups vs. Classes of Compact Spaces

For a given class T of compact Hausdorff spaces, let Y(T ) denote the class of -groups G such that for each g G, the Yosida space Y (g) of g belongs to T . Conversely, if R is a class of -groups, then T(R) stands for the class of all spaces which are homeomorphic to a Y (g) for some g G R. The correspondences T Y(T ) and R T(R) are examined with regard to several closure properties of classes. Several sections are devoted to radical classes of groups whose Yosida spaces are zero-dimensional. There is a thorough discussion of hyper-projectable -groups, followed by presentations on Y(e.d.), where e.d. denotes the class of compact extremally disconnected spaces, and, for each regular uncountable cardinal , the class Y(disc), where disc stands for the class of all compact -disconnected spaces. Sample results follow. Every strongly projectable -group lies in Y(e.d.). The -group G lies in Y(e.d.) if and only if for each g G Y (g) is zero-dimensional and the boolean algebra of component...

• Type: Journal
• Year: 2002
• Where: ORDER
• Authors: Michael R. Darnel, Jorge Martinez
• Keywords: Compact -disconnected Spaces, Compact Hausdorff Spaces, ORDER 2002, Yosida Space